DEVELOPMENT OF A LOCAL SUBGRID DIFFUSIVITY MODEL FOR LARGE-EDDY SIMULATION OF BUOYANCY-DRIVEN FLOWS: APPLICATION TO A SQUARE DIFFERENTIALLY HEATED CAVITY

We present a local subgrid diffusivity model for the large-eddy simulation of natural-convection flows in cavities. This model, which does not make use of the Reynolds analogy with a constant subgrid Prandtl number, computes the subgrid diffusivity independently from the subgrid viscosity along the lines of the mixed scale model for eddy viscosity. First, an a-priori test is performed from a direct numerical simulation (DNS) approach in order to compare the respective effects of the subgrid viscosity model and that introduced by the QUICK scheme used to discretize the convective terms in the momentum equations. Then the subgrid diffusivity model is applied to the case of a two-dimensional square cavity filled with air for a Rayleigh number of 5 2 10 10 . Comparisons with DNS reference results demonstrate significant improvements in capturing the general pattern of the flow and particularly in predicting the transition to turbulence in the boundary layers as compared with Reynolds analogy results. The influence of subgrid diffusivity on the local heat transfer is also examined.     

Two-fluid large-eddy simulation approach for particle-laden turbulent flows

In this paper, effects of particles on the subgrid scales of turbulence are properly accounted for during the modeling of subgrid scale stresses in the large-eddy simulation (LES) of fluid phase. In doing so, we propose closed filtered kinetic equations for phase space density of the particle. The various moments of these equations give the `fluid' equations which can be considered as the LES equations for the particle phase. The influence of subgrid scales motion on the particles is included in these `fluid' equations.     

基于RANS和LES的汽油、柴油及其掺混燃料压燃燃烧特性数值模拟研究

研究中首先采用RANS和LES两种湍流模型对汽油、柴油及汽柴油掺混燃料的喷雾进行了气液相贯穿距的标定。基于标定好的喷雾模型,采用RANS与LES对3种燃料在发动机中的燃烧过程开展了数值模拟研究。通过对比RANS与LES对部分预混燃烧数值模拟的差异,揭示了两种湍流模型对缸内流动、燃料输运及燃烧过程的影响机理。结果表明,RANS与LES都能够对柴油及掺混燃料的燃烧过程实现较好的预测,其中LES对汽油部分预混燃烧中滞燃期及放热规律的预测与试验更为接近。同时,LES对3种燃料NOx排放的计算结果都与试验更加接近,这与燃料在缸内放热的位置密切相关。     

A comprehensive review on numerical approaches to simulate heat transfer of turbulent supercritical CO2 flows

Abstract

Extensive computational investigations have been performed to obtain more detailed information about the peculiar phenomena of turbulent supercritical carbon dioxide (sCO₂) flow as ideal heat transfer fluids in various thermal engineering applications. This paper reviews the simulation techniques used and discusses their advantages, shortcomings and applicability. Not only is a comprehensive inspection on various computational approaches provided, but also the model refinements are suggested. Direct Numerical Simulations (DNS) provides valuable and reliable information about the thermohydraulics of turbulent sCO₂ flows, in particular within the near-wall region, which well interprets the observed heat transfer enhancement and deterioration with property variations, flow acceleration and buoyancy discussed. However, DNS is not feasible when it comes to high Reynolds number flows with complex geometries encountered in practical applications because of the drastically increasing computational cost. Reynolds-Averaged Navier-Stokes (RANS) modeling is able to fill the gap with acceptable accuracy and becomes the mainstream for turbulent sCO₂ heat transfer simulations. The flow and heat transfer behaviors of turbulent sCO₂ can be simulated using RANS modeling leading to acceptable predictions. However, the performance variation is considerable for different models and for the same model of changing operating conditions, model generality is not reached. In addition, some treatments implemented into the RANS models for constant property fluids are not appropriate for variable-property sCO₂ flows, causing inconsistency on the mixed convection predictions. Variable turbulent Prandtl number and more advanced calculation schemes for buoyancy production of turbulent kinetic energy are strongly recommended. Also, more appropriate treatments for damping functions are demanded to enable the model properly respond to the local property changes, particularly near the wall. Much simpler models with far less computational cost based upon the two-layer theory are being developed to achieve the generality. While this is promising, the examinations are still limited to the certain conditions and some model parameters need to be calibrated against the DNS data, which definitely reduces the model universality since DNS only covers a limited range of operating conditions. Developing more generic and reliable RANS models is still the main focus of simulation techniques used for turbulent sCO₂ heat transfer.     

Calibration of the Reynolds Stress Model for the Simulation of Gas Flows in Corrugated Tubes

Tubes with corrugated surfaces can clearly increase the overall heat transfer coefficient in comparison to smooth tubes. Due to the additional influence of different curved surfaces, the analytical calculation of the overall heat transfer coefficient and pressure drop fails for those tubes. Numerical simulations using turbulence models with two or three differential equations appropriate for isotropic turbulence are not satisfactory in this case. Since corrugated walls cause anisotropic turbulences in the near wall region, the secondary flow must be considered in the numerical simulation. Within the time averaging turbulence models (Reynolds averaged Navier stokes = RANS models), the Reynolds stress model (RSM) is the only model solving all six components of the Reynolds stress tensor and thus enabling the consideration of secondary and anisotropic turbulence. Most turbulence models are developed and calibrated for smooth wall boundary conditions. As a consequence, simulations of corrugated tubes based on isotropic turbulence models provide inadequate results when compared with measured values. This article describes the calibration of the RSM for the simulation of corrugated tubes using the values of a shell-and-tube test facility for adaptation. To calibrate the heat transfer rate, the dimensionless turbulent Prandtl number is modified. For the pressure drop calculation, the pressure strain coefficient is adjusted varying the appropriate dimensionless coefficient. Moreover, the local flow behavior in the near wall region is validated by local measurements by laser Doppler velocimetry.     

Derivation of the conditional moment closure equations for spray combustion

In this work we derive the fundamental equations for conditional moment closure (CMC) modelling of individual phases set in a two-phase flow. The derivation is based on the instantaneous transport equations for the single phase that involve a level set/indicator function technique for accounting for interfaces. Special emphasis is put on spray combustion with the CMC equations formulated for the gas phase. The CMC equations are to be viewed as an adjunct to existing methods for the modelling of the dynamics of sprays: they provide a refinement of the modelling of chemical reactions in the gas phase. The resulting CMC equations differ significantly from those already in use in the literature. They contain, of course, unclosed terms that need to be modelled. Investigation of the unclosed terms associated with evaporation at the droplet surface is well beyond the capabilities of laboratory measurement or direct numerical simulation. It is proposed that modelling of these terms be based on the well-established ‘laws’ of similarity between heat and mass transfer: an example is detailed for one example of the general modelling of the spray dynamics. Other unclosed terms are important throughout the gas phase. Models used for these terms in single-phase flows are reviewed and it is proposed that any modifications needed for these models be investigated by DNS of suitable model problems having good resolution of the flow and mixing in the inter-droplet space. It is proposed that a spray analogue of the scalar mixing layer that has been widely studied in single-phase flows be used as the model problem for such DNS studies and also for LES and RANS modelling.     

A FOUR-EQUATION MODEL FOR PREDICTION OF GAS-SOLID TURBULENT FLOWS

A four-equation model is proposed for prediction of dilute turbulent gas-solid flows where the ratio of the particle and the gas densities is large. The model is based on explicit algebraic relations for Reynolds stresses and turbulent fluxes of the void fraction, which were derived in an earlier work within the context of Reynolds-averaged Navier-Stokes (RANS) methodology. These relations are manipulated here to derive nonlinear eddy-viscosity-type models for thin-shear flows. Further, new models are proposed for third-order correlations which are also simplified for thin-shear flows. These models are used to propose four transport equations for the turbulence kinetic energy of the carrier phase and its rate of dissipation, the turbulence kinetic energy of the dispersed phase, and the velocity covariance of the two phases. The final four-equation model is implemented for prediction of a particle-laden turbulent jet, and encouraging agreements with available laboratory data are observed.     

The Computational Modeling of Transitional Flow through a Transonic Linear Turbine: Comparative Performance of Various Turbulence Models

Aero-thermal characteristics of transitional flow through a highly loaded transonic linear turbine are studied at the design incidence using computational methods. The three-dimensional compressible turbulent flow through a turbine inlet guide vane is simulated using finite-volume method-based fluid flow solutions using both Reynolds-averaged Navier Stokes (RANS) equations-based turbulence models, and a dynamic large eddy simulation (LES) approach which is based on a Smagorinsky-Lilly subgrid scale (SGS) model. The calculations are made for exit isentropic Mach numbers ranging from 0.7 to 1.1, and for Reynolds numbers ranging from 5 × 10⁵ to 2 × 10⁶. The numerical results obtained from different turbulence model simulations are compared with each other, and with the experimental data available in the open literature in terms of integrated flow parameters, such as pressure and heat transfer coefficients for varying exit Mach and Reynolds numbers. The present numerical approach indicates a guide line that the present LES approach can be a reliable choice for turbomachinery flows.     

Evaluation of four numerical wind flow models for wind resource mapping

A wide range of numerical wind flow models are available to simulate atmospheric flows. For wind resource mapping, the traditional approach has been to rely on linear Jackson–Hunt type wind flow models. Mesoscale numerical weather prediction (NWP) models coupled to linear wind flow models have been in use since the end of the 1990s. In the last few years, computational fluid dynamics (CFD) methods, in particular Reynolds‐averaged Navier–Stokes (RANS) models, have entered the mainstream, whereas more advanced CFD models such as large‐eddy simulations (LES) have been explored in research but remain computationally intensive. The present study aims to evaluate the ability of four numerical models to predict the variation in mean wind speed across sites with a wide range of terrain complexities, surface characteristics and wind climates. The four are (1) Jackson–Hunt type model, (2) CFD/RANS model, (3) coupled NWP and mass‐consistent model and (4) coupled NWP and LES model. The wind flow model predictions are compared against high‐quality observations from a total of 26 meteorological masts in four project areas. The coupled NWP model and NWP‐LES model produced the lowest root mean square error (RMSE) as measured between the predicted and observed mean wind speeds. The RMSE for the linear Jackson‐Hunt type model was 29% greater than the coupled NWP models and for the RANS model 58% greater than the coupled NWP models. The key advantage of the coupled NWP models appears to be their ability to simulate the unsteadiness of the flow as well as phenomena due to atmospheric stability and other thermal effects. Copyright © 2012 John Wiley & Sons, Ltd.     

Numerical assessment of subgrid scale models for scalar transport in large-eddy simulations of hydrogen-enriched fuels

A comparison of two different models addressing the scalar transport in large-eddy simulations is conducted for a non-reacting jet and an experimental flame. A simple approach based on a gradient diffusion closure is compared against the linear-eddy model in the context of hydrogen-enriched non-reacting fuel jets and flames burning hydrogen-enriched mixtures. The results show that the gradient diffusion model is not valid as a subgrid scale model for large-eddy simulations of mixtures containing hydrogen. It produces unphysical scalar fields with unrealistic temperature distributions. Approaches based on the linear-eddy model can be used instead to obtain appropriate representation of the scalar field and more accurate predictions of the scalar transport and the temperature field.     

火花点燃发动机的2维燃烧模型研究

本文介绍了一套２维内燃机流动燃烧模型，采用了蒸发性液体射流喷雾模型和亚网格尺度（ＳＧＳ）湍流模型，燃烧和排放的计算采用部分平衡流方法。编制了可在微机上运行的内燃机工作过程２维模拟计算程序。并对一台层状充量发动机进行了模拟计算。     

Influence of Turbulence Schmidt Number on Exit Temperature Distribution of an Annular Gas Turbine Combustor using Flamelet Generated Manifold

The Reynolds analogy concept has been used in almost all turbulent reacting flow RANS(Reynoldsaveraged Navier–Stokes)simulations,where the turbulence scalar transfers in flow fields are calculated based on the modeled turbulence momentum transfer.This concept,applied to a lean premixed combustion system,was assessed in this paper in terms of exit temperature distribution.Because of the isotropic assumption involved in this analogy,the prediction in some flow condition,such as jet cross flow mixing,would be inaccurate.In this study,using Flamelet Generated Manifold as reaction model,some of the numerical results,obtained from an annular combustor configuration with the turbulent Schmidt number varying from 0.85 to 0.2,were presented and compared with a benchmark atmospheric test results.It was found that the Schmidt numberσt in mean mass fraction f transport equation had significant effect on dilution air mixing process.The mixing between dilution air and reaction products from the primary zone obviously improved asσt decreased on the combustor exit surface.Meanwhile,the sensitivity ofσt in three turbulence models including Realizable k-ε,SST(Shear Stress Transport)and RSM(Reynolds Stress Model)has been compared as well.Since the calculation method of eddy viscosity was different within these three models,RSM was proved to be less sensitive than another two models and can guarantee the best prediction of mixing process condition.On the other hand,the results of dilution air mixing were almost independent of Schmidt number Sct in progress variable c transport equation.This study suggested that for accurate prediction of combustor exit temperature distribution in steady state reacting flow simulation,the turbulent Schmidt number in steady state simulation should be modified to cater to dilution air mixing process.     

二阶矩亚网格燃烧模型对射流火焰的大涡模拟

用二阶矩亚网格燃烧模型对美国Sandia国家实验室测量甲烷／空气射流火焰进行了大涡模拟(LES),与实验数据和用二阶矩输运方程湍流燃烧模型的雷诺平均(RANS)模拟结果进行了对比．LES得到时间平均的温度, 甲烷浓度以及温度脉动均方根值和实验值符合很好．LES时均值和RANS模拟结果接近,LES脉动均方根值优于 RANS模拟结果．LES瞬态结果显示了有燃烧时的拟序结构比无燃烧时的强,同时拟序结构强化了燃烧,湍流射流火焰呈皱折火焰面的状态．     

Multi-component gas transport in micro-porous domains: Multidimensional simulation at the macroscale

For decades, models based on the Maxwell–Stefan diffusion equations have been used to predict mass transfer of multi-component gases in porous media. However, the validity of these models is restricted to transport processes that are dominated by diffusion and wall-friction. Therefore, a new computational model is presented, which is based on a comprehensive theory of multi-component gas transport. It comprises conservation equations of mass and momentum for each species contained in the gas mixture together with an energy balance for the mixture.The model is intended to be used for investigations on the macroscopic scale. Thus, the local volume averaging technique is applied and friction coefficients, which encompass the full range of Knudsen numbers, are used to describe the drag forces exerted by the pore structure. In the volume averaged energy equation the gas and solid phases are considered a pseudo-homogeneous medium. The resulting set of highly coupled transport equations is implemented in a commercial computational fluid dynamics program. For validation purposes, the mass transfer model is first used to simulate the isothermal diffusion problem in a Loschmidt tube. Then, the simultaneous mass and heat transfer in a porous duct with cooled walls is investigated. In both cases, the numerical results are in very good agreement with experimental data.     

Transient analysis of incompressible flow through a packed bed

The present investigation aims at numerically simulating the temporal energy transport for incompressible flows through a packed bed. The governing equations are formulated according to the volume averaging method. The generalized momentum equation which accounts for the inertial and viscous forces was used to carry out this research, whereas the two-energy equation model was used for simulating the energy transport. The implications of the non-Darcian terms and the thermal dispersion effects on the transient energy transport were explored. Error maps were introduced for a wide range of flow conditions and bed configurations. In addition, the investigation also tackles the applicability of the local thermal equilibrium condition and the one-dimensional approach for studying the thermal response in packed bed.     

A three dimensional exact equation for the turbulent dissipation rate of Generalised Newtonian Fluids

The flow of non-Newtonian fluids is of interest in many biological and industrial applications, including nanofluids. Most of the papers of the literature on turbulent non-Newtonian fluids focused the attention on viscoelastic fluids. In order to make accurate and low cost prediction of turbulent inelastic non-Newtonian fluids, a RANS Generalised Newtonian Fluid (GNF) turbulence model, based on the exact equations for the turbulent variables, is required. In a previous paper of the same authors the exact equations for the turbulent kinetic energy and the dissipation rate have been derived in a two-dimensional (2D) domain, through the introduction of an apparent viscosity equation. The aim of the present paper is to extend the approach to a three-dimensional (3D) domain, giving the full mathematical demonstration of the exact equations.     

Modeling stable thermal stratification and its impact on wind flow over topography

Microscale flow models used in the wind energy industry commonly assume statically neutral conditions. These models can provide reasonable wind speed predictions for statically unstable and neutral flows; however, they do not provide reliable predictions for stably stratified flows, which can represent a substantial fraction of the available energy at a given site. With the objective of improving wind speed predictions and in turn reducing uncertainty in energy production estimates, we developed a Reynolds‐Averaged Navier–Stokes (RANS)‐based model of the stable boundary layer. We then applied this model to eight prospective wind farms and compared the results with on‐site wind speed measurements classified using proxies for stability; the comparison also included results from linear and RANS wind flow models that assume neutral stratification. This validation demonstrates that a RANS‐based model of the stable boundary layer can significantly and consistently improve wind speed predictions. Copyright © 2014 John Wiley & Sons, Ltd.     

A new scalar fluctuation model to predict mixing in evaporating two-phase flows

A scalar fluctuation model for two phase flows is proposed for RANS (Reynolds Average Navier Stokes) simulations. It is a two equation model based on the variance v of the gaseous fuel mass fraction and on the scalar dissipation χ. For each quantity a transport equation is solved. The models developed by Mantel and Borghi [11] and Newman et al. [9] are used to close the transport equation of χ for gaseous flows. These models (and an algebraic closure for χ) are compared to (Direct Numerical Simulation) DNS results obtained by Eswaran and Pope [12] in the case of mixing in a gaseous homogeneous stationary turbulence. To get a correct agreement between the RANS models and the DNS results, we had to adjust some constants in these models. It is shown that with the algebraic model it is not possible to correctly reproduce the trends observed in the DNS. Then, the closure proposed by Demoulin and Borghi [13] for the spray source term in the variance equation is adopted. The modelling of the spray source term in the scalar dissipation equation represents the main theoretical work of this paper. Comparisons between experiments and computations are performed in order to validate the complete model. These comparisons are performed on a Gasoline Direct Injection optical access engine. To make comparisons between computations and experiments possible, it is necessary to filter the computed variance. This procedure allows to account for the filtering performed by the pixels of the CCD camera used in the experiments. The two- equation models of Newman et al. and Mantel and Borghi used with the variance and scalar dissipation source terms proposed in this paper predict a high turbulence to mixing time ratio r=τ_tτ_m=χυ?k during the evaporation of droplets. This high mixing rate allows the model of Newman et al. to correctly reproduce fluctuation levels in the spark zone as well as the intense fluctuation in the spray region, while the model of Mantel and Borghi tends to over-estimate fluctuation levels. On the contrary, the algebraic closure imposes a fixed ratio r of the order of 2, which leads to a very high over-prediction of fluctuation levels. These results show that a two-equation model with appropriate spray source terms is needed for correctly modeling the mixing in two-phase flows.     

Analysis of high-pressure hydrogen, methane, and heptane laminar diffusion flames: Thermal diffusion factor modeling

Direct numerical simulations are conducted for one-dimensional laminar diffusion flames over a large range of pressures (1?P₀?200 atm) employing a detailed multicomponent transport model applicable to dense fluids. Reaction kinetics mechanisms including pressure dependencies and prior validations at both low and high pressures were selected and include a detailed 24-step, 12-species hydrogen mechanism (H₂/O₂ and H₂/air), and reduced mechanisms for methane (CH₄/air: 11 steps, 15 species) and heptane (C₇H₁₆/air: 13 steps, 17 species), all including thermal NO_x chemistry. The governing equations are the fully compressible Navier-Stokes equations, coupled with the Peng-Robinson real fluid equation of state. A generalized multicomponent diffusion model derived from nonequilibrium thermodynamics and fluctuation theory is employed and includes both heat and mass transport in the presence of concentration, temperature, and pressure gradients (i.e., Dufour and Soret diffusion). Previously tested high-pressure mixture property models are employed for the viscosity, heat capacity, thermal conductivity, and mass diffusivities. Five models for high-pressure thermal diffusion coefficients related to Soret and Dufour cross-diffusion are first compared with experimental data over a wide range of pressures. Laminar flame simulations are then conducted for each of the four flames over a large range of pressures for all thermal diffusion coefficient models and results are compared with purely Fickian and Fourier diffusion simulations. The results reveal a considerable range in the influence of cross-diffusion predicted by the various models; however, the most plausible models show significant cross-diffusion effects, including reductions in the peak flame temperatures and minor species concentrations for all flames. These effects increase with pressure for both H₂ flames and for the C₇H₁₆ flames indicating the elevated importance of proper cross-diffusion modeling at large pressures. Cross-diffusion effects, while not negligible, were observed to be less significant in the CH₄ flames and to decrease with pressure. Deficiencies in the existing thermal diffusion coefficient models are discussed and future research directions suggested.